Curved Focus
What are the refractive indices for these two wavelengths of light?
A plano-convex lens has a narrow radius of curvature of 22.5 cm scale on the convex side. When a color code is placed 48.0cm from the lens, the green light of 550 nm wavelength is focused 277cm of the lens and the blue light of 450 nm wavelength is focused 171cm from the target. What are the refractive indices for these two lengths wavelength of light?
♠ let the incident beam is perpendicular to the striking surface of the lens, which is parallel to axis x, the refracted ray in the lens does not change its direction as it reaches the round surface, the surface around the beam to the angle of incidence b1, b2 being output angle wrt the normal to the point of incidence, so n = sin (b2) / sin (b1), where sin (b2) = b2 * e = (1 / R +1 / S +1 / s), R = 22.5 "cm, l = 48cm, l = 277cm, sin (b1) = b1 = e / R, and e <<R for a thin lens, and n ♣ Green = 1 22.5 / 48 22.5 / 277 = 1.55, n = 1 ♣ Blue 22.5 / 48 22.5 / 171 = 1.60;
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